κ-carbide in a high-Mn light-weight steel: precipitation, off...

κ-carbide in a high-Mn light-weight steel:

precipitation, off-stoichiometry and deformation

Von der Fakultät für Georessourcen und Materialtechnik

der Rheinisch-Westfälischen Technischen Hochschule Aachen

zur Erlangung des akademischen Grades einer

Doktorin der Ingenieurwissenschaften

genehmigte Dissertation

vorgelegt von M.Sc.

Mengji Yao

aus Zhuji, VR China

Berichter: Prof. Dr.-Ing. Dierk Raabe

Univ.-Prof. Jochen M. Schneider, Ph.D.

Tag der mündlichen Prüfung: 20. März 2017

Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar

Acknowledgements

The completion of this dissertation would not be possible without the people

mentioned in the following. I would like to express my sincere gratitude

To Prof. Dierk Raabe for offering me this project and providing guidance and

encouragement throughout this work.

To Prof. Jochen M. Schneider for his interest in this work and being my second

supervisor.

To Dr. Pyuck-Pa Choi, Dr. Michael Herbig and Dr. Baptiste Gault for the intensive

discussions and valuable instructions.

To Dr. Emanuel Welsch, Dr. Marta Lipinska-Chwalek, Dr. Christian Liebscher and

Prof. Christina Scheu for their contributions to the transmission electron microscopy

work.

To Dr. Poulumi Dey, Dr. Tilmann Hickel and Prof. Jörg Neugebauer for their help

on ab-initio calculations.

To Dr. Philippe T. Pinard and Dr. Wenwen Song for performing electron probe

micro-analysis and synchrotron x-ray diffraction experiments, respectively.

To Mr. Andreas Sturm and Mr. Uwe Tezins for their support on the focused ion

beam and atom probe tomography.

To Dr. Hauke Springer, Mr. Frank Rütters and Mr. Frank Schlüter for the material

synthesis and processing.

To Ms. Monika Nellessen, Ms. Katja Agenendet and Ms. Heidi Bögershausen for

their support to the metallography lab and scanning electron microscopy devices.

To all colleagues from Max-Planck-Institut für Eisenforschung GmbH, especially

in the group of “Atom Probe Tomography” and in the office room 688, for the lovely

working atmosphere and daily interactions.

To my family and friends for their understanding and support all along this path.

To the funding from European Research Council under the EU’s 7th Framework

Programme (FP7/2007-2013)/ERC Grant agreement 290998 “SmartMet”.

Contents

Symbols and abbreviations .......................................................................................... i

1 Introduction ............................................................................................................ 1

2 Materials and methods .......................................................................................... 6

2.1 Material processing ........................................................................................... 6

2.2 Microstructure characterization ......................................................................... 7

2.2.1 Synchrotron X-ray diffraction .................................................................. 7

2.2.2 Scanning electron microscopy ................................................................. 8

2.2.3 Transmission electron microscopy .......................................................... 9

2.2.4 Atom probe tomography .......................................................................... 9

2.2.5 Correlative transmission electron microscopy and atom probe

tomography .......................................................................................................... 12

2.3 Density functional theory study ...................................................................... 15

3 Dislocation-particle interaction during plastic deformation ............................ 17

3.1 Introduction ..................................................................................................... 17

3.2 Results .............................................................................................................. 19

3.2.1 Morphology and arrangement of κ-carbides .......................................... 19

3.2.2 Dislocation/κ-carbide interaction ........................................................... 21

3.3 Discussion ...................................................................................................... 26

3.3.1 Particle shearing and ordering strengthening ......................................... 26

3.3.2 Particle dissolution and solute segregation ............................................ 28

4 Elemental partitioning and κ/ interface structure ........................................... 31

4.1 Introduction ................................................................................................... 31

4.2 Results ........................................................................................................... 32

4.2.1 κ/ elemental partitioning and phase compositions ................................ 32

4.2.2 κ/ interface structure ............................................................................. 37

4.3 Discussion ...................................................................................................... 44

4.3.1 Compositional accuracy of APT measurements .................................... 44

5 Off-stoichiometry and site-occupancy of κ-carbides ......................................... 60

5.1 Introduction ................................................................................................... 60

5.2 Results ........................................................................................................... 61

5.2.1 APT-based analysis of site-occupancy ................................................... 61

5.2.2 DFT-based investigations of off-stoichiometry and site-occupancy ...... 71

5.3 Discussion ...................................................................................................... 76

5.3.1 Off-stoichiometry and site-occupancy of κ-carbides ............................. 76

5.3.2 Underlying issues related to DFT ........................................................... 78

6 Phase equilibria in the κ/ microstructure ......................................................... 80

6.1 Introduction ................................................................................................... 80

6.2 Results ........................................................................................................... 81

6.2.1 Prolonged-aged microstructure .............................................................. 81

6.2.2 Coarsening of grain interior precipitates ................................................ 85

6.2.3 Grain boundary discontinuous precipitation .......................................... 89

6.3 Discussion ..................................................................................................... 97

6.3.1 Influence of strain state on the off-stoichiometry of κ-carbides ............ 97

6.3.2 Thermal stability of coherent GI κ-carbide precipitates ........................ 98

6.3.3 Grain boundary discontinuous precipitation .......................................... 99

7 Summary and outlook ....................................................................................... 107

7.1 Summary ..................................................................................................... 107

7.2 Outlook ........................................................................................................ 109

Bibliography ............................................................................................................. 110

List of tables .............................................................................................................. 121

List of figures ............................................................................................................ 123

Curriculum Vitae ..................................................................................................... 131

Abstract ..................................................................................................................... 133

Zusammenfassung .................................................................................................... 135

i

Symbols and abbreviations

Symbols

Ferrite

Lattice misfit

True strain

pPartitioning coefficient

Austenite

𝛾𝐴𝑃𝐵

Anti-phase boundary energy

’ Gamma-prime phase in superalloys

κ Kappa-carbide

μ Chemical potential

Diffraction angle

𝜎 Stress

r Particle radius

a Lattice parameter

b Burgers vector

c Composition

d{hkl} Interplanar distance of the {hkl} lattice planes

D Diffusion coefficient

E Formation energy

ii

f Mole fraction

G Shear modulus

kB Boltzmann constant

M Taylor factor

t Time

T Temperature

Vf Volume fraction

X Diffusion length

Z Atomic number

Abbreviations

1D One-dimensional

2D Two-dimensional

3D Three-dimensional

APB Anti-phase boundary

APT Atom probe tomography

BSE Backscattered electron

DF Dark field

DP Discontinuous precipitation

EBSD Electron backscatter diffraction

ECCI Electron channeling contrast imaging

EDX Electron dispersive x-ray spectroscopy

EPMA Electron probe microanalysis

ER Evaporation rate

fcc Face-centered cubic

FEG Field emission gun

FM Ferromagnetic

FIB Focused ion beam

FOV Field-of-view

GB Grain boundary

GI Grain interior

HAADF High angle annular dark field

iii

HAGB High angle grain boundary

HR High-resolution

LEAP Local electrode atom probe

LRO Long-range ordering

MBIP Microband-induced plasticity

OM Optical microscopy

OPS Oxide polishing suspension

PF Pulse fraction

RDF Radial distribution function

ROI Region of interest

SAD Selected area diffraction

SDM Spatial distribution map

SE Secondary electron

SEM Scanning electron microscopy

SFE Stacking fault energy

SIP Shear-band induced plasticity

SQS Quasi random structure

SRO Short-range ordering

SS Solid-solution

STEM Scanning transmission electron microscopy

SXRD Synchrotron X-ray diffraction

TEM Transmission electron microscopy

TOF Time-of-flight

TRIP Transformation induced plasticity

TWIP Twinning induced plasticity

XRD X-ray diffraction

ZA Zone axis

1

Chapter 1

Introduction

There is a strong demand for the development of advanced high-strength steels for

automotive applications, in order to reduce energy consumption and greenhouse gas

emission. Austenitic () high-Mn (15-30 wt.%) Fe-Mn-Al-C steels show particularly

outstanding mechanical properties (Frommeyer et al., 2006; Chang et al., 2010;

Springer et al., 2012; Gutierrez-Urrutia et al., 2013; Park et al., 2013; Raabe et al., 2014;

Rana et al., 2014) and are therefore highly promising candidates for such applications.

Due to their good oxidation and corrosion resistance (Banerji et al., 1978), these steels

were originally developed in an attempt to substitute Cr-containing stainless steels, but

recently they have regained substantial interest due to their excellent strength-ductility

balance and significantly reduced mass density because of alloying with Al.

Austenitic Fe-Mn-Al-C steels, containing high Al (5-12 wt.%) and high C (0.5-1.3

wt.%), are age-hardenable. Through an ageing treatment at a temperature of 470-710 °C

(Sato et al., 1989; Tjong et al., 1990; Sato et al., 1990; Choo et al., 1997), nanometer-

scale ordered κ-carbide precipitates can be introduced into the disordered face-centered

cubic (fcc) austenite matrix, which can remarkably strengthen the material while

preserving great ductility. Due to the great importance of κ-carbide precipitates,

numerous studies have been conducted to understand their precipitation and

deformation behavior, which, however, are not fully clear.

Chapter 1. Introduction

2

Pronounced planar slip is generally observed in deformed κ-carbide-containing -

alloys (Gutierrez-Urrutia et al., 2013; Park et al., 2013; Raabe et al., 2014; Welsch,

2016). Though a few transmission electron microscopy (TEM) micrographs of sheared

particles have been reported (Choi et al., 2010; Welsch, 2016), controversial opinions

still exist over the predominant interaction mechanism between κ-carbide precipitates

and dislocations. Gutierrez-Urrutia et al. concluded that the primary mechanisms are

Orowan bypassing of particle stacks and subsequent expansion of dislocation loops

assisted by cross-slip (Gutierrez-Urrutia et al., 2014). Since the κ-carbide precipitates

are finely dispersed in the -matrix, it is challenging to make a clear observation of them

in the presence of dislocations. The current existing two-dimensional (2D) TEM

micrographs are not convincing enough.

Moreover, no matter which mechanism dominates, a better microstructural

characterization is yet necessary to quantitatively analyze the strengthening behavior.

As for the “Orowan looping” case, the particle size and inter-spacing are critical which

however are not unambiguous in 2D projected micrographs. In the case of “particle

shearing”, besides particle size, its feasibility is associated with the antiphase boundary

(APB) energy on the slip plane (Ardell et al., 1988), which depends on the stoichiometry

and site-occupancy of the ordered particle.

Commonly, the composition of κ-carbides is given as (Fe,Mn)3AlCx, where the

exact chemical composition of this phase is still unknown (Sato et al., 1988; Tjong,

1990; Sato et al., 1990; Choo et al., 1997). It is tacitly assumed to be a derivative from

the Fe3AlCx-type ternary κ-carbide (Oshima et al., 1972). Due to the difficulty in

determining C concentrations in small precipitates and also obtaining single-phase κ-

carbide, the exact composition of the Fe3AlCx-type κ-carbide was uncertain for a long

time (Palm et al., 1995; Sanders et al., 1997). In 1995, Palm et al. revealed a

composition range for this phase between Fe3.2Al0.8C0.71 and Fe2.8Al1.2C0.42, i.e.

Fe3+yAl1-yCx (-0.2


3

few nanometers in size, their direct chemical characterization is challenging. Atom

probe tomography (APT) is the ideal tool to resolve this composition uncertainty since

it offers near-atomic spatial resolution and equal detection sensitivity to all elements

(Miller et al., 1996; Gault et al., 2012b; Larson et al., 2013; Miller et al., 2014).

However, in contrast to intensive studies on κ-carbide-containing alloys, little APT data

have been published on κ-carbide precipitates in quaternary austenitic Fe-Mn-Al-C

alloys.

The crystal structure of κ-carbides is reported to be L’12 perovskite-type (Tjong,

1986; Tjong, 1990; Han et al., 1986; Choo et al., 1985). In such a variant of the

conventional fcc crystal structure, the unit cell contains 5 atoms at 3 kinds of sites. In

addition to the 4 atoms at one corner and three face-centered sites, as per fcc

conventional unit cell, there is also one atom at the body-centered site. Conventionally,

as shown in Figure 1.1, the elemental site-occupancy of the κ-carbide phase is such that

Al occupies the corner site of the unit cell, Fe and Mn the face-centered positions, and

C occupies the body-centered octahedral interstitial site, which is based on observations

of electron diffraction patterns and calculations of structure factors (Tjong, 1986; Han

et al., 1986; Tjong, 1990). In terms of atomic percentage, the stoichiometric

(Fe,Mn)3AlC κ-carbide has 60% (Fe+Mn), 20% Al and remaining 20% C. However,

the κ-carbides are commonly expected to be off-stoichiometric and thus the elemental

site-occupancy remains unresolved.

Figure 1.1. Schematic sketch of the unit cell of the ideal stoichiometric (Fe,Mn)3AlC

L’12 κ-carbide with Fe, Mn, Al and C atoms shown by red, orange, green and purple

balls, respectively.


4

In addition, nanometer-sized κ-carbide precipitates are often regarded as coherent

particles with respect to the -matrix according to x-ray diffraction (XRD) analyses

(Huang et al., 1994) or simply tacitly assumed. The interfacial structure between κ-

carbide precipitate and -matrix is little known, which, however, could significantly

affect the morphology and arrangement of κ-carbide precipitates due to elastic constrain

if any and the dislocation motion if misfit dislocation occurs.

Besides the beneficial intragranular precipitation of κ-carbide, detrimental

intergranular precipitation of coarse κ0-carbide via discontinuous precipitation (DP) has

also been noticed in Fe-Mn-Al-C alloys (Chao et al., 1993; Hwang et al., 1993; Huang

et al., 1994; Choo et al., 1997; Kimura et al., 2004). The resultant lamellae colonies,

composed of κ0-carbide and other solute-depleted phase(s), gradually wipe out the GI

structure by GB migration. Though the DP product phases were identified in these

works, the initiation and evolution of such a phase transition has not been investigated.

From the mechanical performance perspective, it is of great importance to understand

this process. Also, from a thermodynamic point of view, the phase equilibria and

elemental partitioning in such a microstructure need a better understanding.

To address the questions discussed above, a quaternary model Fe-29.8Mn-7.7Al-

1.3C (wt.%) steel was chosen in this work. An ageing treatment at 600 °C was utilized

for the κ-carbide precipitation. The well-precipitated 24 hours-aged sample was

subjected to tensile deformation in order to study the deformation mechanisms. Given

that the nanometer-sized κ-carbide precipitates are dense and chemical analysis is

compulsory for the phase composition and elemental partitioning study, three-

dimensional (3D) APT is the optimal tool for the κ-carbide characterization, thus

employed as the primary technique. Besides, synchrotron x-ray diffraction (SXRD),

high-resolution scanning electron microscopy (SEM) and (scanning) transmission

electron microscopy ((S)TEM) are also utilized to obtain a general overview of the

microstructure or complementary information to APT results. Theoretical calculations

in the framework of density functional theory (DFT) is additionally employed to

understand the atomistic structure of the off-stoichiometric κ-carbide.

This thesis is organized in the following way.

Chapter 1: Introduction.


5

Chapter 2: Materials and methods. The details of material synthesis and thermos-

mechanical processing is introduced in this chapter. The devices and methods

utilized in this work for microstructure characterization and the theoretical

approach are described in detail.

Chapter 3: Dislocation-particle interaction during plastic deformation. In this chapter,

the 3D morphology and arrangement of κ-carbides in -matrix are firstly studied by

APT and the κ/ alloy deformed to different strains are studied via correlative TEM

and APT technique, revealing the dislocation-particle interaction mechanism.

Chapter 4: Elemental partitioning and κ/ interface structure. In this chapter, the κ/

elemental partitioning and chemical compositions of κ/ phases are studied by APT,

the compositional accuracy of which is discussed. The κ/ interfacial structure, in

terms of chemical gradient, interfacial width and coherency, are investigated using

SXRD, STEM and APT.

Chapter 5: Off-stoichiometry and site-occupancy of κ-carbide. In this chapter, attempts

are made to resolve the site-occupancy of off-stoichiometric κ-carbide from both

the experimental and theoretical perspective. DFT calculations successfully predict

the off-stoichiometry and explains such a phenomenon.

Chapter 6: Phase equilibria in the κ/ microstructure. In this chapter, the prolonged-

aged κ/ microstructure is characterized via SXRD, SEM and APT, revealing the

co-existence of coherency equilibrium of GI κ/ phases and thermodynamic

equilibrium of GB κ0/0/α-ferrite phases. The thermal stability of GI κ-carbide and

initiation & evolution mechanisms of GB κ0/0/α-ferrite phases are discussed.

Chapter 7: Summary and outlook.

6

Chapter 2

Materials and methods

2.1 Material processing

A high-Mn Fe-30Mn-8Al-1.3C (wt.%) steel was synthesized as a rectangular bar

(12 kg, thickness of 40 mm) via melting and casting in an induction furnace under argon

atmosphere. Due to evaporation of the melt and its interaction with the crucible during

the production process, extra amounts of the alloying elements were added in order to

achieve a target composition. According to empirical experience, a Fe-30.8Mn-8.2Al-

1.34C alloy was produced aiming at the final Fe-30.0Mn-8.0Al-1.3C composition (all

in wt.%). The composition of the as-cast alloy, as determined by wet chemical analysis,

is listed in Table 0.1.

Table 0.1. Chemical composition of the studied alloy obtained by wet chemical analysis.

Fe Mn Al C

wt.% 61.2 29.8 7.74 1.28

at. % 53.9 26.7 14.12 5.25

In order to remove microstructural heterogeneities inherited from the solidification

process, the cast ingot was reheated to 1200 °C for 30 min and subsequently hot-rolled

at 1100 °C to a thickness reduction of 75%, followed by water-quenching. The bar

sample of 11×11×60 mm3, cut from the hot-rolled sheet, was then subjected to a solid-

Chapter 2. Materials and methods

7

solution (SS) treatment at 1200 °C for 2 h in a furnace under argon atmosphere and

quenched to room temperature in an oil bath. At 1200 °C, the alloy is fully austenitic

(Chin et al., 2010).

To induce the precipitation of κ-carbides and study their evolution and phase

stabilities upon ageing, the SS-treated sample was isothermally annealed at 600 °C for

various times from 24 hours up to three months and oil quenched. The aged samples

are referred to ‘x-aged’, where ‘x’ indicates the ageing time.

The 24h-aged alloy with well-precipitated nanometer-scale κ-carbides was chosen

as a representative case for the study on the dislocation-particle interaction during

plastic deformation. Cylindrical tensile test samples with a gauge dimension of Φ 6

mm×40 mm were prepared and interruptedly tested to true strains of ε=0.02, 0.05 and

0.15 in a Zwick ZH 100 tensile machine with an initial strain rate of 5×10-4 s-1.

2.2 Microstructure characterization

Microstructure characterization of various samples was conducted using multi-

scale techniques, including synchrotron X-ray diffraction (SXRD), optical microscopy

(OM), scanning electron microscopy (SEM), transmission electron microscopy (TEM)

and atom probe tomography (APT).

2.2.1 Synchrotron X-ray diffraction

Due to the high coherency between the κ-carbide precipitates and -austenite

matrix (Sato et al., 1988; Sato et al., 1989; Sato et al., 1990; Tsay et al., 2011), i.e. little

lattice misfit, as well as potential grain boundary (GB) phases formed in small amounts

(Chao et al., 1993; Hwang et al., 1993), it is difficult to identify phases and trace their

evolution upon ageing by laboratory X-ray diffraction. High-resolution SXRD with a

superior signal-to-background ratio was hence employed. Thin cylindrical film samples

of 3 mm in diameter were machined from alloys under different ageing states and

mechanically grinded by SiC abrasive papers of grits from 120 up to 2000 (European

P-grade) till reaching a sample thickness of ~1 mm. The SXRD measurements were

carried out by Wenwen Song from the Lehrstuhl und Institut für Eisenhüttenkunde

(IEHK), Rheinisch-Westfälische Technische Hochschule Aachen (RWTH Aachen) at


8

the high-resolution powder diffraction beamline P02.1 PETRA III Bessy with a

wavelength of 0.20727 Å. The detected 2D diffraction patterns were first calibrated and

integrated into one-dimensional (1D) data (intensity versus 2θ) by the software Fit2D

(Hammersley et al., 1994) and further analyzed by the Rietveld method using the

software MAUD (Lutterotti et al., 1999).

2.2.2 Scanning electron microscopy

Samples for microscopy studies were all prepared following the standard

metallographic procedure:

firstly, grinded by SiC abrasive papers of grit from 120 up to 4000 (European P-

grade) under flowing water;

then mechanically polished using 3 μm-grained diamond suspension with

lubricant;

finally, polished by colloidal silica oxide polishing suspension (OPS) with a few

drops of soap to remove mechanically induced surface deformation and ensure a

clean surface.

For the sake of simplicity during sample preparation and handling, disc samples

machined from gauges of tensile test samples were embedded into thermosetting

bakelite with carbon filler of standard cylindrical geometry (Φ 25 mm) by a hot-

mounting process under 180 °C and 25 kN (Struers PolyFast). To better reveal the

multi-phase microstructure, some samples were etched with a 1% Nital solution (a

mixture of nitric acid and ethanol) for 30-90 seconds. Prior to electron microscopy

analysis, OM was often used to get a rough overview of the microstructure.

Further microstructural characterization was performed in two field emission gun

(FEG) HR-SEMs, i.e. JEOL JSM 6500F (JEOL GmbH) and ZEISS Crossbeam XB

1540 (Carl Zeiss SMT AG), both operated at 15 kV and equipped with EDAX electron

backscatter diffraction (EBSD) system. The ZEISS microscope was mainly employed

for secondary electron (SE) and backscattered electron (BSE) imaging, whereas most

EBSD measurements were carried out in the JEOL tool. The EBSD data was acquired

and analyzed using the TSL OIM software (version 6.5-7.0).


9

2.2.3 Transmission electron microscopy

TEM was employed for nanometer-sized precipitate analysis. The TEM work,

including phase analysis by selected area diffraction (SAD) and precipitate observation

using dark-field (DF) imaging, was mainly completed by Emanuel Welsch from the

Department of Microstructure Physics and Alloy Design, Max-Planck-Institut für

Eisenforschung GmbH (MPIE) and reported in his PhD dissertation (Welsch, 2016).

Marta Lipinska-Chwalek from the Peter Grünberg Institut (PGI), Forschungszentrum

Jülich also kindly helped for Scanning-TEM (STEM) measurements on the coherency

of κ-carbide precipitate with respect to the -matrix in a FEI Titan G2 80-200

ChemiSTEM operated at 200 kV.

High angle annular dark field (HAADF) STEM samples were prepared by focused

ion beam (FIB) using two FIB/SEM dual beam devices - FEI Helios Nano-Lab 600 and

FEI Helios Nano-Lab 600i. Since the κ-carbides have a {001} cube-cube orientation

relationship with the -matrix (Choo et al., 1997), is the optimal direction for an

edge-on view of the κ/ interface, which was therefore adopted as the primary analysis

axis. Moreover, for a fcc-metal, dislocation slip is typically activated along

directions on {111} planes, whose edge-on observation direction would be .

Hence, thin lamellas for misfit dislocation study were prepared along {001} and {011}

planes, i.e. lifted out along {001} and {011} plane traces in a {100}-oriented grain

(plane normal), respectively. The aim of orientation-specific preparation is to simplify

TEM operation, i.e. minimizing the tilting required to achieve target zone axes and the

increase in sample thickness caused by tilting. The crystallographic directions of bulk

samples for lift-out were determined by prior EBSD measurements. The FIB-prepared

lamellae were first cleaned by oxygen plasma for 30 seconds before performing STEM

studies.

2.2.4 Atom probe tomography

TEM/STEM is good at crystallography, phase identification, defect and strain

analysis down to atomic scale whereas it is difficult to map the distribution of light

elements like carbon with electron dispersive x-ray spectroscopy (EDX). TEM images

are also 2D projections of a 3D microstructure, which could also cause an ambiguous


10

interpretation of precipitate morphologies and alignments. Alternatively, APT, a

combination of ion projection microscopy and a time-of-flight (TOF) spectroscopy, has

a near-atomic resolution with equal sensitivity to all elements (Gault et al., 2012b). It

was thereby employed for a three-dimensional (3D) chemical mapping of the

nanometer-sized κ-carbides embedded in the -matrix.

Needle-shaped APT specimens were all prepared by FIB using the two FIB/SEM

dual beam devices as mentioned above. The usual lift-out procedure (Thompson et al.,

2007) was employed for most specimens. To minimize the Ga implantation into

specimens, during specimen sharpening the ion beam energy was reduced from 30

kV/~0.26 nA to 16 kV/~0.14 nA after the 1st annular ion milling step and 2 kV/ ~24 pA

was adopted for the final cleaning.

For GB studies, it is challenging to prepare a specimen with a GB in the analysis

volume since GBs are probably inclined with respect to sample surface and not visible

by FIB/SEM during annual ion milling. To increase the success rate of capturing a GB,

the GB was aligned parallel to the analysis direction by a tilted lift-out and then simply

kept as the center of the annular milling patterns. A pre-cutting deep into the bulk

sample across GB was first made to obtain the GB inclination angle, i.e. the angle

between the GB and the bulk sample’s surface. During the lift-out, the stage was then

tilted by an angle complementary to the GB inclination angle, which directly made the

GB perpendicular to the specimen post (parallel to the analysis direction).

During the analysis of the reaction front of GB discontinuous precipitation (DP),

considering the field-of-view (FOV) of an APT specimen is much larger longitudinally

than laterally, the reaction front was oriented perpendicular to the analysis direction by

the method described in (Felfer et al., 2012), to enlarge the analysis volume in front of

and behind the reaction front. Commercial Mo-grids (1GM 100, Pyser-SGI) were used

as specimen posts in this case to realize the 90° rotation, simply by switching the Mo-

grid holder adaptor with two perpendicular stage-mounting pins. The preparation of

Mo-grids and its corresponding special home-made holder and holder adapters for FIB

and APT instruments are explained in detail in (Herbig et al., 2015a).

Two local electrode atom probe (LEAP) devices were used in this work for APT

measurements. The LEAP 3000X-HR (CAMECA instruments) with a reflectron has a

detection efficiency of ~37% while the LEAP 5000X-S (CAMECA instruments), a


11

straight path system, has a high detection efficiency of ~80%. Atom probe instrument

equipped with a reflectron is usually expected to have improved mass resolutions (the

peak width in a mass spectrum normalized by the mass of the peak) (Cerezo et al.,

1998). Most measurements were performed in the LEAP 3000X-HR tool. The LEAP

5000X-S was used for a comparable study on the mass spectra and crystallography.

Needle-shaped specimens were measured in voltage-pulsing mode at ~70 K with a

pulse repetition of 200 kHz, a pulse fraction (PF) of 15% and a target evaporation rate

(ER) of 5 ions per 1000 pulses. Choosing such a set of parameters is based on a detailed

study of the influence of measurement parameters on phase compositions, which will

be explained in detail in section 4.3.1.2. The collected APT data were reconstructed and

analyzed using the IVAS software (version 3.6.6 - 3.6.14) by CAMECA instruments.

Figure 2.1. APT mass spectrum of κ-carbide containing austenitic alloy obtained by

LEAP 3000X-HR: (a) 5-15 Da, (b) 18-26 Da, (c) 26-30 Da, (d) 33-57 Da. Ranges of

mass-to-charge-state ratios without peaks are omitted. Peaks with ion overlap are

marked with constituent ions.

Figure 2.1 shows a representative mass spectrum of the studied austenitic alloy

with κ-carbide precipitation. Peaks at 6, 6.5, 12, 13 Da are identified as carbon


12

monomers. Apart from them, several peaks can be assigned to carbon molecular ions,

similar to previous studies on other high-C containing alloys and carbides (Miyamoto

et al., 2012; Marceau et al., 2013; Takahashi et al., 2011; Li et al., 2011; Kitaguchi et

al., 2014; Thuvander et al., 2011). Peaks at 18, 18.5, 36 and 37 Da belong to carbon

trimer ions. The carbon dimers 12C21+ and (13C12C)1+ are detected at 24 and 25 Da,

respectively. The presence of 24.5 Da peak, which can be assigned to (13C12C3)2+,

indicates the detection of carbon tetramers (Takahashi et al., 2011; Li et al., 2011; Sha

et al., 1992). Hence, the peak at 24 Da does not only result from the carbon dimer 12C21+

but also partly from 12C4 2+. This overlapped peak can be decomposed by considering

the peak at 24.5 Da (13C12C3)2+. According to the natural abundance of carbon isotopes

12C and 13C, the contribution of 12C42+ to peak 24 Da can be estimated by its relative

abundance ratio to (13C12C3)2+ (Takahashi et al., 2011; Li et al., 2011; Sha et al., 1992).

The decomposition via the IVAS software indicates that 12C42+ gives a contribution of

about 37% to the peak at 24 Da. The 12C22+ peak could in principle overlap with the

12C1+ peak at 12 Da. However, the absence of a peak belonging to (12C13C)2+ suggests

that there is a negligible fraction of 12C22+ at the peak at 12 Da. Regarding substitutional

elements, Fe2+ is detected at 27, 28, 28.5 and 29 Da and its primary isotope can also be

detected at 56 Da (56Fe+) and 18.7 Da (56Fe3+). Mn2+ is detected at 27.5 Da. Peaks at 9

and 13.5 Da can be ascribed to Al3+ and Al2+, respectively. Here, it is also noted that

according to the natural abundance of the isotopes of Fe, the peak at 27 Da cannot be

completely assigned to 54Fe2+. Al1+ ions must give a contribution to it as well (Seol et

al., 2012; Seol et al., 2013). The peak decomposition algorithm in IVAS indicates that

45% of this peak can be assigned to Al1+. The measured total impurity concentration Si

(14 Da) and Cr (26 Da) is less than 0.1 at.%. The material is a rather clean quaternary

Fe-Mn-Al-C model alloy.

2.2.5 Correlative transmission electron microscopy and atom probe

tomography

The particle-matrix interface and deformed microstructure of the 24h-aged alloy

were further studied by the correlative TEM/STEM and APT approach (Herbig et al.,

2015a). Although APT is capable of mapping a 3D microstructure with sub-nm

resolution, due to different evaporation fields of κ-carbides and -austenite, local


13

magnification could occur and complicate the 3D reconstruction of the κ/ interface

(Gault et al., 2012b). Also, it is often difficult to resolve crystal defects, such as

dislocations and slip bands, only by APT due to the lack of the crystallographic

information. Combining TEM/STEM and APT enables a correlative and

complementary understanding on the interface structure and particle-dislocation

interaction.

Electro-polished Mo-grids were used as specimen posts for the correlative study,

which could be easily transferred between FIB, TEM and APT with a grid holder

(Herbig et al., 2015a). Similar to STEM lamella analysis, to optimize the measurement

conditions, needle-shaped specimens are preferred to be orientation-specific. Due to the

{001} cube-cube κ/ orientation relationship, the specimens for κ/ interface study were

prepared orthogonally along -directions and put into a double-tilting TEM holder

in such a way that the (α, β) tilting axes and electron beam were all parallel to the

direction. Thereby the electron beam would directly observe edge-on the {001} κ/

interface. Also, there would be κ/ interfaces perpendicular to the APT analysis

direction, minimizing the local magnification effect during field evaporation and

utilizing the higher resolution along the in-depth direction (Gault et al., 2012b). Owing

to the dense distribution of the κ-carbides, there are often enough precipitates for

interface analysis within the FOV of STEM and APT, i.e. ~80 nm from apex, beyond

which the specimen thickness would be too large for STEM analysis.

In contrast, the correlative study on slip bands is challenging in terms of specimen

preparation. Due to the limited FOV of APT and common premature failure of

deformed APT specimen, the slip bands have to be within the top ~100 nm from the

needle’s apex in order to be detected in APT before a specimen facture. This is

challenging since there is no image contrast of slip bands at all during annular FIB

milling. For heavily deformed samples, e.g. ε=0.15, it is possible to realize that, owing

to the high density of slip bands with an average spacing of ~250 nm, as well as the

activation of multiple groups of slip bands (Welsch, 2016). However, the slip bands in

slightly deformed samples (ε


14

exposure during the zone axes search process affecting the specimen survival rate in

subsequent APT measurements, an orientation-specific specimen is desirable.

The optimal direction for observing particle shearing along typical {111} fcc slip

planes is . The strategies employed for such a specimen preparation are as

follows.

Prior EBSD and electron channeling contrast imaging (ECCI) (Zaefferer et al.,

2014) were utilized to search for one set of {011} dense sharp slip lines in a {011}-

oriented grain (done by Emanuel Welsch). Slip lines parallel to the longest {011}

plane trace were preferred since they are less inclined from the sample surface, i.e.

with a higher probability of being captured in the analysis volume.

The relative distance and angle between the slip lines and microstructural features

such as GB and inclusions, which could be visible by FIB/SEM, were measured.

The target set of slip lines was located by FIB/SEM according to its relative

position with respect to the microstructural features.

The lift-out was carried out in such a way that the long-axis of the wedge was

perpendicular to the slip lines.

Specimens prepared in this way would directly fit the TEM zone axis (ZA)

and should include several inclined slip bands in the top volume. The subsequent

TEM characterization could manifest the distance between slip bands and needle

apex and a further controlled FIB re-sharpening could bring the target slip band to

the FOV of APT measurement.

In order to minimize beam contamination and surface oxidation, all the specimens

were freshly prepared just before loading into TEM double-tilting holders. Christian

Liebscher from Department of Structure and Nano-/ Micromechanics of Materials,

MPIE and Marta Lipinska-Chwalek performed STEM measurements on κ/ interface

in a probe-corrected FEI Titan 80-300 S/TEM microscopy operated at an accelerating

voltage of 300 kV. The TEM observation on deformed specimens was done by Emanuel

Welsch in a Philips CM20 device. After the TEM work, the specimens were directly

transferred into the FIB for re-sharpening when necessary and a re-cleaning at 2 kV for

a few seconds to remove the contamination and oxidized layer before APT

measurements.


15

2.3 Density functional theory study

To understand the site-occupancy of ordered κ-carbide and the influence of elastic

strain on its stoichiometry, ab-initio work was employed in this work. Poulumi Dey and

Tilmann Hickel from Department of computational materials design, MPIE performed

the calculations using density functional theory (DFT) as implemented in the Vienna

Ab Initio Simulation Package (VASP) (Kresse et al., 1993). Projector augmented wave

(PAW) potentials were used to describe the electron-ion interaction (Blöchl, 1994). The

generalized-gradient approximation (GGA) functional of Perdew, Burke and Ernzerhof

(PBE) (Perdew et al., 1996) was employed. The single-electron wave functions were

expanded using plane waves up to an energy cut-off of 500 eV. The Methfessel-Paxton

method (Methfessel et al., 1989) was used for the Fermi surface smearing with a 6×6×6

Monkhorst-Pack grid for 2×2×2 atomic supercells of both stoichiometric and off-

stoichiometric κ-carbides. The energies converged to a precision of 1 meV/atom.

Structural relaxations were performed until the forces on each atom were below 0.01

eV/Å. Cell shape and atomic positions were fully relaxed in all calculations, unless

specified otherwise.

The 2×2×2 supercell of stoichiometric (Fe,Mn)3AlC κ-carbide is composed of 8

unit cells in the L’12 structure with 5 sites/unit cell and occupied by 40 atoms

((Fe16Mn8)Al8C8). Here, Fe/Mn are situated at face-centered sites of each unit cell, Al

at corner sites and C atoms occupy the body-centered octahedral sites (Figure 2.2(a)).

An Fe to Mn ratio of 2:1 was employed based on the APT results. DFT studies reveal

that configurational entropy is more favorable than chemical ordering in the face-

centered Fe/Mn sub-lattice of κ-carbide above ~75 K (Dey et al., 2016). The Fe/Mn

chemical disorder was taken into account by a special quasi-random structure (SQS)

generation scheme (Zunger et al., 1990) for the 2×2×2 supercell. It is important to note

that all calculations were performed for ferromagnetic (FM) κ-carbide since the (Mn)

anti-site formation energies computed for FM and paramagnetic states differed only by

a small amount (~0.05 eV). Therefore, the consideration of paramagnetism, which is

computationally much more demanding, does not qualitatively alter the results on

structural properties and estimated point defect concentrations in κ-carbide (Dey et al.,

2016).


16

Figure 2.2. Schematic visualization of the supercell of (a) stoichiometric L’12 κ-carbide,

(Fe16Mn8)Al8C8, and (b) off-stoichiometric κ-carbide with a Mn anti-site at the Al sub-

lattice and C vacancies, (Fe16Mn8)(Mn1Al7)(C5Vac3), with chemical disorder in the

Fe/Mn sub-lattice with an Fe:Mn ratio of 2:1. Fe, Mn, Al and C atoms are shown by

red, orange, green and purple balls, respectively. The theoretical calculations were done

by Poulumi Dey and Tilmann Hickel.

17

Chapter 3

Dislocation-particle interaction

during plastic deformation

3.1 Introduction

A common characteristic of alloys showing excellent strength and ductility is a

pronounced strain hardening capability, which continuously increases the strength and

delays local necking during deformation. Transformation induced plasticity (TRIP) and

twinning induced plasticity (TWIP) steels are typical examples for alloys showing high

strain hardening capabilities (Herrera et al., 2011; Gutierrez-Urrutia et al., 2011), where

martensitic transformation and formation of deformation twins are the respective

dominant deformation and strain hardening mechanisms. The active deformation

mechanisms are closely related to the stacking fault energy (SFE). Generally, as the

SFE increases, the dominant deformation mechanism changes from TRIP to TWIP and

from TWIP to dislocation gliding (Allain et al., 2004; Pierce et al., 2014).

Gutierrez-Urrutia et al. attributed the excellent strain hardening capacity of solid

solution austenitic Fe-Mn-Al-C alloys containing 5 wt.% Al, intragranular precipitation of nanometer-sized κ-carbides leads to a

Chapter 3. Dislocation-particle interaction during plastic defromation

18

substantial increase in yield strength without a significant loss in ductility. Planar

dislocation substructures were observed in deformed κ-carbide containing austenitic Fe-

M-Al-C alloys. The occurrence of planar dislocation substructures in these alloys,

which have high SFE values ranging from 80 to 110 mJ/m2 (Park et al., 2013), was

ascribed to shearing of ordered κ-carbides by dislocations and a mechanism referred to

as “glide plane softening” (Gerold et al., 1989). According to this mechanism, the local

order is destroyed by a leading dislocation shearing the ordered particle and thus

facilitating the glide of consecutive trailing dislocations. For high strain levels, the

mechanisms of shear-band-induced plasticity (SIP) (Frommeyer et al., 2006) and

microband-induced plasticity (MBIP) (Yoo et al., 2009; Park et al., 2013) have been

suggested, referring to homogeneous shear deformation and bands of very high

dislocation density, respectively.

However, the interaction between dislocations and κ-carbide precipitates in age-

hardened austenitic Fe-Mn-Al-C steels is still not well understood. Debates still exist

over the dominant co-deformation mechanism during plastic deformation, i.e. the

competition between dislocation looping and precipitate shearing. Choi et al. claimed

that κ-carbide precipitates are sheared by slip bands since misalignment of particle

stacks was observed along a specific direction by TEM DF imaging (Choi et al., 2010).

However, Gutierrez-Urrutia et al. suggested that Orowan bypassing of stacks of κ-

carbides is predominant, followed by expansion of dislocation loops by cross-slip while

shearing of κ-carbides occurs only rarely (Gutierrez-Urrutia et al., 2014). Convincing

observations are still missing to illustrate the dislocation interaction with κ-carbide

precipitates. The answer to this question is the prerequisite to understand the nature of

the strengthening by κ-carbide precipitates and thereby accurately predict the yield

strengths of the precipitation-hardened κ/ alloys.

This chapter aims at providing a comprehensive understanding of the interaction

of dislocations with κ-carbide precipitates, as well as the associated strengthening and

deformation mechanisms. First of all, the 3D morphology and arrangement of κ-carbide

precipitates in the non-deformed -matrix are unveiled by APT analysis. Then

correlative TEM-APT analyses are employed to systematically characterize the

deformed κ/ microstructure under various strain states. Crystallographic and chemical

mapping are correlated to each other, demonstrating the dislocation interaction with κ-


19

carbide precipitates. Finally, the strengthening effect of κ-carbide precipitates, how they

are affected by plastic deformation and its reverse effects on deformation are discussed.

The 24h-aged sample is chosen for this work as a state, for which precipitation is

pronounced and is similar to the previously reported, typical κ/ microstructure (Choo

et al., 1997; Choi et al., 2010; Sato et al., 1988-1990; Tjong et al., 1990).

3.2 Results

3.2.1 Morphology and arrangement of κ-carbides

Precipitation of coherent κ-carbides in the -matrix introduces an elastic stress

field due to the lattice mismatch between precipitates and matrix (Choo et al., 1997).

The shape and arrangement of κ-precipitates are determined by the minimization of the

sum of the elastic energy and the interfacial energy, arising from the κ/ phase

boundaries (Doi et al., 1996).

Figure 3.1(a) shows the ordered L’12-type κ-carbide precipitates within the

austenitic matrix observed by APT. The κ-carbides in the reconstructed 3D atom maps

are visualized by 9 at.% C iso-concentration surfaces. APT reveals that cuboidal and

plate-like κ-carbide particles are arranged in 3D in the form of stacks along three

orthogonal directions which are identified by TEM observations as the elastically soft

crystallographic directions (Gutierrez-Urrutia et al., 2012; Gutierrez-Urrutia et

al., 2014; Choo et al., 1997). The cuboidal particles have a size of 15-20 nm. The largest

cross-sections of plate-like particles perpendicular to the particle stack directions are

often square-shaped with an edge length of 15-20 nm, while the thickness of the plates

is on the order of 5-10 nm. The spacing between two parallel stacks is on the order of

10-40 nm and will be referred to as broad -channels. The spacing between individual

precipitates within a stack is about 2-5 nm and will be referred to as narrow -channels.

Figure 3.1(b) shows a schematic sketch of -carbide precipitates’ 3D morphology

and arrangement based on APT observations. Two possible corresponding 2D transect-

projections along zone axes, which are often employed for imaging -carbides

with TEM, are shown in Figure 3.1(c). Particles that might be assumed to have a

cuboidal morphology based on their square-like appearance in the TEM DF images


20

(Gutierrez-Urrutia et al., 2012; Gutierrez-Urrutia et al., 2014; Choo et al., 1997) have

very often a much smaller size in the third dimension according to APT. Thus, they

show plate-like morphology (see the particles outlined in red). At the intersection

between two stacks of precipitates a preference for a cuboidal morphology is often

observed, e.g. the particles outlined in green. Long rectangular particles observed in

TEM micrographs (particles highlighted in yellow outlines) are found to be rectangular

parallelepipeds.

Figure 3.1. Morphology and arrangement of κ-carbide precipitates in 3D space (APT)

and 2D observation (e.g. TEM): (a) three representative reconstructed 3D APT maps of

C (purple), Al (green) and Mn (yellow) atoms. The κ-carbide precipitates are visualized

with a 9 at.% C iso-concentration surface. (b) A schematic illustration of the 3D

morphology and arrangement of κ-carbide precipitates based on APT observations. (c)

2D projections of the κ/ microstructure along directions highlighted in (b),

simulating the TEM observation.


21

3.2.2 Dislocation/κ-carbide interaction

Figure 3.2. TEM dark-field (DF) images of deformed microstructures at different true

strains of (a) ε=0.05 and (b) ε=0.15 utilizing the superlattice diffraction spot of κ-

carbides. Two different zone axes (ZA) (a) [011] and (b) [001] were employed to show

the shearing of κ-carbides and sheared κ-carbides, respectively. The TEM

measurements were carried out by Emanuel Welsch.

The deformed microstructure of the 24h-aged samples are shown in Figure 3.2,

which displays TEM micrographs obtained from APT specimens. The TEM

observations were obtained by Emanuel Welsch. At a low strain level of 0.05, clear

shearing of κ-carbide stacks is observed along the [011] ZA as indicated by arrows in

Figure 3.2(a). The κ-carbide precipitates have a (001) cube-cube orientation relationship

with the -matrix. Along the [011] ZA, i.e. looking edge-on the (11 1̅) plane, the

nanometer-sized κ-carbides with a 2-5 nm inter-spacing in the narrow -channels


22

overlap with each other in the 2D TEM projection. Instead of individual precipitates, a

stack of precipitates is observed. The misalignments of several stacks along a single slip

line is captured (Figure 3.2(a)), clearly revealing the shearing of κ-carbides by slip. As

the true strain increases to 0.15, more slip systems are activated and intensive slip bands

appear (highlighted by arrows in Figure 3.2(b)), which, along the [001] ZA, are

manifested by dense precipitate fragments concentrating on certain directions. In

comparison to the relatively complete precipitates at the apex of the needle-shaped

specimen, the κ-carbide precipitates within these slip bands are fragmented into small

debris. At the intersection of slip bands, the superlattice phase contrast is almost

completely lost, indicating either the loss of ordering or even dissolution of precipitates.

It is worth noting that from low-strain to high-strain states, slip bands are observed

throughout the specimens, not only in these two representative ones shown in the Figure

3.2, but also in another approx. 10 specimens. Particle shearing is a general phenomenon,

observed in the deformed κ/ microstructure, and therefore believed to be the prevalent

deformation mechanism. The previous debates in the literature on either shearing or

Orowan looping is probably due to the lack of clear observation of such deformed

microstructures. The high density of particles and specific crystallographic orientation

add difficulties onto that. Here, these difficulties are circumvented by optimized

specimen preparation, adopting thin needle-shaped specimens specifically oriented with

the help of a prior EBSD measurement.

The deformed microstructure with 3D chemical mapping, accomplished by

correlative TEM -APT on a 0.05-strained specimen, is presented in Figure 3.3. In the

TEM micrograph (Figure 3.3(a)), two originally cuboidal or plate-like κ-carbide

precipitates are clearly split into two parts - one major part and another smaller one at

the corner, as highlighted by blue arrows. The slight mismatch between these two parts,

particularly for the right plate-like κ-carbide, indicates that these two precipitates are

sheared by dislocation slip. The slip directions of the two precipitates are parallel to

each other. Since the needle-shaped specimen is prepared orthogonally along the

direction, the slip direction can be characterized as ~45° from [001] and [010], i.e. close

to [011]. Besides, as highlighted by yellow arrows, there are also some small fragments

of the ordered precipitates, which probably have been heavily fragmented by

deformation.


23

Figure 3.3. Correlative TEM and APT analysis of a deformed microstructure at a true

strain of ε=0.15: (a) TEM dark-field (DF) micrograph along [001] zone axis with the

blue arrows highlighting the shearing of κ-carbides and yellow ones indicating the

fragments of κ-carbides; (b) an overlay of reconstructed APT analysis volume with

purple κ-carbides visualized by carbon iso-concentration surface at a threshold value of

9.0 at.% on top of the TEM DF micrograph of the same specimen taken before APT

measurement; (c-e) 3D elemental atom maps of the reconstructed APT volume with

different elemental iso-concentration surfaces of (c) C 9.0 at.%, (d) C 7.5 at.% and

(e) Al 14.5 at.%, showing the dissolution of κ-carbides. The TEM measurements were

carried out by Emanuel Welsch.

The same specimen was subsequently analyzed by APT. Figure 3.3(b) shows an

overlay of the reconstructed APT analysis volume on top of the DF-TEM micrograph.

The latter utilizes the superlattice diffraction contrast to reveal the ordered κ-carbide

precipitates whereas the former employs carbon iso-concentration surfaces at a

threshold value of 9.0 at.% to show the carbon-enriched κ-carbides. The size, shape and

position of κ-carbide precipitates in the reconstructed APT volume fit well with the DF-

TEM image, illustrating that the employed APT reconstruction algorithm, tip profile


24

reconstruction, could perform properly for this κ/ alloy. Despite the well reconstructed

APT volume, particle splitting by dislocation slip is not clearly observed, conversely to

what was highlighted by blue arrows in the DF-TEM image (Figure 3.3(a)). This is

probably due to shearing of the precipitate by a single dislocation glide rather than dense

slip bands of high dislocation density, as captured in the TEM micrograph. The signal

is likely smoothed out by voxelization and delocalization of APT data. Instead of two

split parts of one precipitate, only one complete κ-carbide is visualized by carbon iso-

concentration surface in the APT volume. In addition to large κ-carbides both observed

in TEM and APT, there are also small, irregularly shaped fragments with no obvious

visual match between TEM and APT measurements: the region of which is marked by

a yellow dash circle in Figure 3.3(b). Some fragments observed in the DF-TEM image

are not found in APT analysis via 9.0 at.% C iso-concentration surface, and vice versa.

This is probably due to the limited FOV of APT so that the outer shell of the specimen

observed in TEM are not registered at the APT detector (Herbig et al., 2015a). Or the

κ-carbides at this region fragmented by deformation preserve local ordering and solute

enrichment to some extent, but not necessarily both at the same time.

To better reveal the 3D solute distribution after deformation, further APT

elemental maps and iso-concentration surfaces of different elements at varying

threshold values are created (Figure 3.3(c-e)). As highlighted by a black dashed circle

in Figure 3.3(c), the elements are not homogeneously distributed at this region. A lower

threshold value for the C iso-concentration surface of 7.5 at.% unveils that there are not

only small C-enriched fragments but also C segregation along certain directions, as

indicated by black arrows in Figure 3.3(d). Such a linear solute enrichment is also

correspondingly found for Al at the same positions (Figure 3.3(e)), but not for Mn (not

shown here). Completely differing from the common particle morphology (Figure 3.1),

these line features imply that the κ-carbides in this region have been fragmented and

dissolved during deformation. The dislocation slip might destroy the κ-carbides and

drag the solutes along with its movement. Considering the affinity between segregated

solutes and crystalline defects (Kirchheim et al., 2007), it is highly possible that the

solute segregation zones are dislocation lines. The reason why such an enrichment only

takes place for Al and C, not Mn, is that the κ-carbides are enriched with Al and C, not

Mn (details for κ/ elemental partitioning are referred to Chapter 4.2.1).


25

Owing to the -oriented specimen, as well as the (001) cube-cube orientation

relationship between κ-carbide precipitates and -matrix, the directions can be

easily figured out for the reconstructed 3D APT analysis volume (Figure 3.4). Therefore,

a crystallographic analysis can be performed on the linear solute segregation zones,

highlighted by black arrows in Figure 3.3(d).

Figure 3.4. Crystallographic analysis of three solute-segregated line features in a

deformed κ/ alloy at a true strain of 0.15 as highlighted by black arrows in Figure 3.3(d)

based on the orientation of the needle-shaped specimen.


26

All three line segregation zones (Figure 3.4(a), (b) and (c)) are well associated to

{111} planes, which are the typical slip plane for fcc metals. Along with the

aforementioned slip direction (Figure 3.3(a)), the activated slip system can be

identified as {111}, that is the typical slip system for fcc metals. Among these

three linear segregation zones, one line is found to be perpendicular to the slip

direction (Figure 3.4(a)) and the other two are inclined to that (Figure 3.4(b)(c)), which

implies that probably the former is an edge dislocation while the latter have a mixed

character.

3.3 Discussion

3.3.1 Particle shearing and ordering strengthening

The microstructure of the 24h-aged alloy deformed to different strain states have

been studied by correlative TEM and APT. It is revealed that {111} dislocation

slip and shearing of κ-carbide precipitates occurs during plastic deformation rather than

Orowan looping.

The ordered κ-carbide with a L’12-type perovskite structure deform differently

from the disordered fcc -matrix. For dislocation slip on a crystallographic plane, a

shear stress, the so-called Peierls stress, has to be exerted on the slip plane, which

depends exponentially on the ratio of lattice spacing d to the Burgers vector b and

thereby ought to be smallest for a slip along the close-packed direction on the close-

packed plane (Gottstein, 2004). In disordered fcc , this corresponds to the

a/2{111} slip system (a is the lattice parameter). However, in chemically ordered

L’12 κ-carbides the preferred slip system could be a{001} or a{111}, since

the shortest lattice vectors a do not lie in the close-packed {111} planes.

Experimentally, the observed activated slip system is the latter one. Given that the

Burgers vector of a perfect dislocation in the -matrix (a/2) is only half of the

closing vector to restore the ordered κ-carbide to its perfect lattice, it cannot enter the

κ-carbide unless a planar defect is formed (Ardell, 1985; Reed, 2008). A pair of

superpartial a/2{111} dislocations must travel together through the κ-carbides,

forming the so-called superdislocation. The resultant planar fault in-between two


27

superpartials is known as an anti-phase boundary (APB) and the APB energy 𝛾𝐴𝑃𝐵

represents the associated energy barrier for the occurrence of particle cutting.

Depending on 𝛾𝐴𝑃𝐵, volume fraction Vf and the mean particle radius r (assumed

spherical for simplicity) of the κ-carbides, the pair of superpartial dislocations could

reside in the same κ-carbides or there could be faulted particles between the leading and

trailing superpartials, i.e. ‘strongly coupled’ or ‘weakly coupled’ superpartials,

respectively (Reed, 2008). Their anticipated order strengthening contribution are

different considering the elastic stress between the superpartials. In the SS-treated alloy,

free of precipitates, the spacing between the superpartials intersecting the short-range

ordering (SRO) was found to be ~20 nm (Welsch et al., 2016). Since the APB energy

is usually relatively high and should be much higher in the 24h-aged alloy with κ-

carbide precipitates of long-range ordering (LRO) than that in SS-treated alloy, the

superpartials would experience more resistance in the κ-carbide containing alloy. The

superpartial spacing should be less than ~20 nm and comparable to the particle size.

Hence, the superdislocation in this case is more inclined to strong-coupling, whose

ordering strengthening contribution is

∆𝜎𝑜𝑟𝑑𝑒𝑟𝑖𝑛𝑔 = √3

2 𝑀 (

𝐺𝑏

𝑟) 𝑉𝑓

1

2 𝑤

𝜋32

(2𝜋 𝛾𝐴𝑃𝐵 𝑟

𝑤 𝐺 𝑏2− 1)

1

2, (3.1)

where M is the Taylor factor of 3.06 to convert the resolved shear strength for

dislocation motion into an equivalent uniaxial yield strength of a polycrystal (Stoller et

al., 2000), G represents the shear modulus, b denotes the Burgers vector and w is a

dimensionless constant of the order of unity. No 𝛾𝐴𝑃𝐵 data is reported specifically for

κ-carbides, but similarities with superalloys with a L12 ordered structure and the

activated {111} slip system (Reed, 2008)) allow us to use values reported for

those alloys (𝛾𝐴𝑃𝐵 ~0.1 J/m2) as a rough estimate. Taking G=70 GPa, b=0.26 nm

(Welsch et al., 2016), r=10 nm (half of the particle size ~ 20nm) and 𝑉𝑓 ~0.21

(experimental results refer to section 4.2), ∆𝜎𝑜𝑟𝑑𝑒𝑟𝑖𝑛𝑔 is estimated to be 321 MPa. This

is much lower and more reasonable than what is estimated for Orowan stress

∆𝜎𝑂𝑟𝑜𝑤𝑎𝑛~𝑀 𝐺 𝑏 √𝑉𝑓

𝑟=2.55 GPa (Gottstein, 2004), supporting that particle cutting is the

preferred mechanism rather than Orowan bypassing.

Experimentally, the ageing-introduced κ-carbides was found to significantly

increase the yielding strength of the alloy by ~480 MPa (Welsch, 2016). Given that the


28

two samples, SS-treated and 24h-aged, have similar grain sizes and the solute

concentration is lower in the aged alloy as a result of precipitation, the order

strengthening contribution, estimated as 321 MPa for κ-carbide shearing, is relatively

low in comparison to the strength increase of ~480 MPa. One reason could be that there

are additional contributions arising from the elastic strain field due to coherency, shear

modulus mismatch between κ-carbide precipitates and -matrix, and creation of

additional matrix-precipitate interface during particle shearing (Ardell, 1985). On the

other hand, a few assumptions are made for the estimation of order strengthening.

Firstly, for the sake of simplicity, the κ-carbides are assumed to be homogeneously

distributed. In fact, as shown in Figure 3.1, they form particle stacks with different

widths for broad and narrow -channels. Locally, along the particle stacks, the volume

fraction is much higher than the averaged ~0.21. Secondly, there is actually no reported

data of 𝛾𝐴𝑃𝐵 for κ-carbides. ~0.1 J/m2 is only based on the ’ precipitates in superalloys

with a similar crystal structure and a similar slip system, which may lead to an

inaccurately estimated strength increase.

3.3.2 Particle dissolution and solute segregation

Despite having a high SFE, the 24h-aged alloy exhibits pronounced planar slip

during deformation (Welsch, 2016). It has been ascribed to the so-called glide plane

softening phenomenon, which states that the cutting of ordered precipitates on a single

slip plane by superdislocations results in a continuous decrease of obstacle strength on

this individual plane and only minor strength needs to be overcome by the following

dislocation pairs until all particles of the activated slip plane are completely cut (Gerold

et al., 1989). Thereby, dislocation motion and particle shearing is restricted to the slip

plane, giving rise to the planar slip with isolated active slip planes. As strain increases,

multiple slip bands are activated and the spacing between slip bands is continuously

reduced (Welsch, 2016). The refinement of planar slip bands progressively destroys the

κ-carbides (Figure 3.2-3.3). Inside the slip bands, particularly at their intersections, κ-

carbides are found fragmented or even dissolved.

Similar dissolution of shearable particles under plastic deformation has been

reported in severe plastic deformed metals, e.g. dissolution of metastable fine

precipitates in equal-channel angular pressed Al alloys (Murayama et al., 2001;


29

Gutierrez-Urrutia et al., 2005), and in fatigued metals, e.g. precipitate dissolution within

the persistent slip bands or shear bands (Vogel et al., 1982; Vinogradov et al., 2002).

In those cases, the intensive strain, either applied by severe deformation or accumulated

by cycling, cut the particles into smaller nanoscale fragments, leading to the instability

of the phase because of high surface energy and their eventual dissolution. Such a

particle fragmentation is also observed in the present κ/ alloy by massive slip bands in

high-strain states (Figure 3.2-3.3), which promotes the dissolution of κ-carbides.

It is known, on the other hand, that the dislocation interaction with solute atoms

of precipitates might also cause the dissolution or decomposition of particles. One well-

studied case is the cementite decomposition in heavily drawn pearlitic steels (Li et al.,

2011). During the motion of dislocations, looping around the interfaces in that case,

carbon atoms are dragged out of the cementite and segregate to dislocation structures.

As for shearable particles, the penetration of dislocations through particles might lead

to the transfer of interstitial atoms from the particles to the matrix due to drifting of

atoms under the stress field of dislocations (Sagaradze et al., 1997). In the present case,

the observed solute-segregated line features are likely dislocations, the crystallographic

orientations of which follows the typical fcc slip system (Figure 3.4). A compositional

analysis of such a segregation is illustrated in Figure 3.5 using proxigram (proximity

histogram, Hellman et al., 2000) and 1D concentration profile. Figure 3.5(b) shows the

proxigram generated around the line segregations highlighted in purple in Figure 3.5 (a)

by a 7.5 at.% C iso-concentration surface. The 1D concentration profiles of cylindrical

regions of interest (ROIs) placed perpendicular to dislocation lines, as shown in Figure

3.5(a), are plotted in Figure 3.5(c-d). Both methods clearly reveal the enrichment of C

and Al to the dislocation lines, the enrichment factor of which are about 2.8 and 1.2 in

comparison to the neighborhood compositions, respectively. This result suggests that

upon particle cutting, indeed the solutes of the κ-carbide precipitates are dragged along

with the moving dislocations, which facilitates precipitate fragmentation and

dissolution. Regarding the composition, no obvious difference is observed between the

two solute-segregated dislocation lines in Figure 3.5(c) and Figure 3.5(d), which are

probably of edge and mixed characters according to the analysis in Figure 3.4(a) and

Figure 3.4(b), respectively.


30

Figure 3.5. Concentration analysis on solute segregation to dislocations: (b) Proxigram

of the magenta-highlighted interface generated by a carbon iso-concentration surface of

7.5 at.% in (a). (c)(d) Two individual 1D concentration profiles of cylindrical regions

of interest (ROIs) perpendicular to two dislocation lines as highlighted in (a).

31

Chapter 4

Elemental partitioning and κ/

interface structure

4.1 Introduction

The precipitation of nanometer-sized κ-carbides in austenitic Fe-Mn-Al-C alloys

significantly strengthens these grades while maintaining substantial formability. This is

realized by a dramatic increase in yield strength and an excellent strain hardening ability

comparable to that of κ-carbide-free alloys (Welsch, 2016). Since particle-shearing is

found to be the dominating deformation mechanism, the significant strengthening effect

results from ordering strengthening, as well as contributions of coherency, shear

modulus mismatch and creation of additional matrix-precipitate interface (section 3.3.1).

In order to better understand the strengthening and strain hardening behavior of the

studied alloy, it is essential to analyze the internal κ/ microstructure, especially the

elemental partitioning and the interfaces between the precipitates and the matrix.

The partitioning of solutes is decisive for the lattice misfit between the κ-carbides

and the -matrix. In a coherent system, elastic strain energy arises from this mismatch

and the precipitates experience an elastic strain field. The critical influence of the elastic

strain field on resultant morphology and arrangement of coherent precipitates has been

noticed in many alloy systems (Doi, 1996; Lee, 1996). As the lattice misfit increases,

Chapter 4. Elemental partitioning and κ/ interface structure

32

the shape of the particles may evolve from sphere to cube and plate, or even needle. The

corresponding elastic anisotropy can lead to a directional alignment of particles instead

of a random distribution. In this chapter, APT is employed for the chemical mapping of

the κ/ microstructure at the atomic scale, illustrating the elemental partitioning between

phases and measuring the chemical composition of κ-carbides. The initial state before

ageing (SS-treated) and the 24h-aged alloy with well-developed κ-carbides are

investigated. To ensure the compositional accuracy of APT measurements, the

influence of measurement parameters on apparent compositions are systematically

studied and the measurement conditions are optimized.

Commonly, κ-carbides are regarded as coherent precipitates according to their

nanometer-scale sizes observed by DF-TEM imaging and small lattice parameter

difference with that of the -matrix based on XRD measurements (Sato et al., 1988;

Choo et al., 1997; Bartlett et al., 2014). To my knowledge, there is no direct atomic-

scale observation of the κ/ interface with respect to compositional and structural

transitions. Due to the small lattice misfit between the κ-carbides and -matrix, the κ-

peaks often appear close to the -peaks as small shoulders. Thus, an accurate

determination of the lattice misfit between κ and is challenging. Moreover, to

understand the non-uniform anisotropic κ/ microstructure (section 3.2.1), the interfaces

between cuboidal/plate-like κ-carbides and broad/narrow -channels have to be

individually studied. Possibly existing local incoherency cannot be detected via XRD.

The existence of misfit dislocation at some point, however, could interact with mobile

dislocations and affect their movement. Hence, another primary aim of this chapter is

to gain a thorough view of the κ/ interfaces at the atomic scale. SXRD is used for an

accurate evaluation of lattice misfit; APT and HAADF-STEM are exploited to study

the interface structure.

4.2 Results

4.2.1 κ/ elemental partitioning and phase compositions

The reconstructed 3D elemental maps for the SS-treated specimens are shown in

Figure 4.1(a). All elements, i.e. Fe, Mn, Al and C, are homogeneously distributed


33

throughout the specimen without any sign of clustering or phase separation. For a better

assessment of the homogeneity of the elemental distributions, nearest neighbor (NN)

distributions (Gault et al., 2012b) are evaluated (Figure 4.1(b)), where the

experimentally measured distributions are compared against artificially randomized, i.e.

correlation-free datasets. For the first as well as higher order NN distribution analyses,

the experimental frequency histograms show a very good match with ideal random

distributions for all detected elements. No elemental partitioning is detected for the SS-

treated state. However, in the same SS-treated alloy, Welsch observed weak superlattice

diffraction spots in TEM and finely dispersed ordered regions in a size of


34

Table 4.1. Chemical compositions (at.%) of supersaturated single austenitic SS-treated

specimens cnand -carbides cand -matrix c in the 24h-aged specimens determined

by APT. Error bars indicate compositional fluctuations between different APT

measurements, where the statistical errors are negligible.

Fe Mn Al C

cn 52.6±0.3 24.5±0.5 17.0±0.2 5.9±0.3

c 43.4±0.3 23.7±0.3 19.8±0.2 13.2±0.4

c 53.8±0.2 25.8±0.3 16.1±0.1 4.3±0.2

After isothermal ageing at 600°C for 24 hours, κ-carbide precipitates are clearly

observed both in TEM as ordered particles (Welsch, 2016) and in APT as a C-enriched

phase (Figure 4.2(a), delineated by a C iso-concentration surface at a threshold value of

9.0 at.%). Figure 4.2(b) shows a 1D concentration profile along a particle stack through

a cylindrical ROI, which is highlighted in green in Figure 4.2(a). Al and C atoms clearly

partition to the κ-carbides, whereas Mn exhibits only slight partitioning to . In order to

closely compare the elemental partitioning of smaller plate-like and larger cuboidal κ-

carbides with respect to their neighborhoods, proxigrams are employed to calculate the

concentrations at fixed distances from their respective iso-concentration surfaces (9 at.%

C). Figure 4.2(c) depicts proxigrams from one large cuboidal κ-carbide κ1L and three

small plate-like κ-carbides κ1S, κ2

S and κ3S, which are highlighted in blue in Figure

4.2(a). The proxigrams of the plate-like particles show slightly higher statistical errors

due to smaller probed volumes as compared to the large cuboidal κ-carbide, but no

compositional difference related to precipitate size and shape is observed. All

compositional profiles are rather smooth and symmetric. No elemental segregation or

pile-up at κ/ interfaces is noticed.

When evaluating phase compositions, contributions from overlapping mass-to-

charge peaks must be considered. Those are however not taken into account in the

above-shown concentration profiles and proxigrams. For a more accurate composition

analysis, decomposition of overlapping mass-to-charge peaks has to be performed.

Hence, phase compositions were determined by clipping out the phases in the 3D atom

maps by iso-concentration surfaces and subsequently analyzing their individual mass

spectra by decomposition of overlapping mass peaks (C2+/C4

2+ and Al+/ Fe2+).


35

Threshold values for iso-concentration surfaces that isolate the κ-carbides and -matrix

were chosen as 10 at.% C and ≤7 at.% C, respectively. These values correspond to the

respective plateau of the C concentrations in κ and in the 1D concentration profiles

and exclude the interfacial region from the analyses (Figure 4.2(b)). Since no

compositional differences were found between κ-carbides of different size and shape,

an average composition value from a

κ-carbide in a high-Mn light-weight steel: precipitation, off...

Documents

Transcript of κ-carbide in a high-Mn light-weight steel: precipitation, off...